After defining rational numbers, one of the ways to define the irrational numbers is by partitioning the rationals into two groups--those less than a certain irrational, and those greater. So, for instance, the square root of two would be defined by the two sets {-1, 0, 1/2, 1, 1.4, 1.41, etc.} and {1.415, 1.42, 1.5, 3, etc.}. I like to think of Dedekind cuts as where numbers stop being rational, and start being Real. All this to preface my suggestion for the slogan--